While Dynkin diagrams are useful for classifying Lie algebras, it is the root and weight diagrams that are most often used in applications, such as when describing the properties of fundamental particles. This paper illustrates how to construct root and weight diagrams from Dynkin diagrams, and how the root and weight diagrams can be used to identify subalgebras. In particular, we show how this can be done for some algebras whose root and weight diagrams have dimension greater than 3, including the exceptional Lie algebras \(F_4\) and \(E_6\).
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